**Rule 17:**- To build a fraction is the reverse of reducing the fraction. Instead of searching for the 1 in a fraction so that you can reduce, you insert a 1 and build.

**Example 3:**- Create a fraction with 40 in the denominator that is equivalent to the fraction .
**Answer:**- The answer is the fraction .
**Solution:**- This problem is a little more difficult because you can't multiply 50 by an integer to get 50. So we will first reduce the initial fraction.
Reduce . .

is equivalent to . (You can verify this with your calculator.)

Recall that you can multiply any number by 1 without changing the value of the number. (Rule 6).

Multiply the fraction by 1.

Recall that 1 has many forms, look for the form of 1 that will result in a denominator of 40.Since 5 8 = 40, use the fraction as 1.

Now can be written as . The product is .We have created a fraction with a denominator equal to 40 that is equivalent to the fraction .

**Check:**- Now prove to yourself with your calculator that your answer is correct. Calculate 80 divided by 50 and calculate 64 divided by 40; both should yield the same answer. If you are correct, the answers are the same (equivalent) and you have successfully built a fraction.

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